MinT - Best Known (14−5, 14, s)-Nets in Base 4

Best Known (14−5, 14, s)-Nets in Base 4

Digital (9, 14, 240)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁴, 240, F₄, 5, 5) (dual of [(240, 5), 1186, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(4¹⁴, 481, F₄, 5) (dual of [481, 467, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁴, 482, F₄, 5) (dual of [482, 468, 6]-code), using
    - trace code [i] based on linear OA(16⁷, 241, F₁₆, 5) (dual of [241, 234, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (9, 14, 245)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁴, 245, F₄, 5) (dual of [245, 231, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁴, 482, F₄, 5) (dual of [482, 468, 6]-code), using
  - trace code [i] based on linear OA(16⁷, 241, F₁₆, 5) (dual of [241, 234, 6]-code), using
    - a code by Danev and Olsson [i]

There is no (9, 14, 3861)-net in base 4, because

1 times m-reduction [i] would yield (9, 13, 3861)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 67 123486 > 4¹³ [i]